rcompshf.cc

ARPACK is a collection of Fortran77 subroutines designed to solve large scale eigenvalue problems.

/*
   ARPACK++ v1.0 8/1/1997
   c++ interface to ARPACK code.

   MODULE RCompShf.cc.
   Example program that illustrates how to solve a complex
   standard eigenvalue problem in shift and invert mode 
   using the ARrcCompStdEig class.

   1) Problem description:

      In this example we try to solve A*x = x*lambda in shift and
      invert mode, where A is derived from the central difference 
      discretization of the 1-dimensional convection-diffusion operator
                         (d^2u/dx^2) + rho*(du/dx)
      on the interval [0,1] with zero Dirichlet boundary conditions.

   2) Data structure used to represent matrix A:

      class ARrcCompStdEig requires the user to provide a way to
      perform the matrix-vector product w = OPv, where OP =
      inv[A - sigma*I]. In this example a class called CompMatrixB was
      created with this purpose. CompMatrixB contains a member function,
      MultOPv, that takes a vector v and returns the product OPv in w.

   3) The reverse communication interface:

      This example uses the reverse communication interface, which
      means that the desired eigenvalues cannot be obtained directly
      from an ARPACK++ class.
      Here, the overall process of finding eigenvalues by using the
      Arnoldi method is splitted into two parts. In the first, a
      sequence of calls to a function called TakeStep is combined
      with matrix-vector products in order to find an Arnoldi basis.
      In the second part, an ARPACK++ function like FindEigenvectors
      (or EigenValVectors) is used to extract eigenvalues and
      eigenvectors.

   4) Included header files:

      File             Contents
      -----------      -------------------------------------------
      cmatrixb.h       The CompMatrixB class definition.
      arrscomp.h       The ARrcCompStdEig class definition.
      rcompsol.h       The Solution function.
      arcomp.h         The "arcomplex" (complex) type definition.

   5) ARPACK Authors:

      Richard Lehoucq
      Kristyn Maschhoff
      Danny Sorensen
      Chao Yang
      Dept. of Computational & Applied Mathematics
      Rice University
      Houston, Texas
*/

#include "arcomp.h"
#include "arrscomp.h"
#include "cmatrixb.h"
#include "rcompsol.h"


template<class T>
void Test(T type)
{

  // Creating a complex matrix (n = 100, shift = 0, rho = 10).

  CompMatrixB<T> A(100, arcomplex<T>(0.0,0.0), arcomplex<T>(10.0,0.0));

  // Creating a complex eigenvalue problem and defining what we need:
  // the four eigenvectors of A nearest to 0.0.

  ARrcCompStdEig<T> prob(A.ncols(), 4, arcomplex<T>(0.0, 0.0));

  // Finding an Arnoldi basis.

  while (!prob.ArnoldiBasisFound()) {

    // Calling ARPACK FORTRAN code. Almost all work needed to
    // find an Arnoldi basis is performed by TakeStep.

    prob.TakeStep();

    if ((prob.GetIdo() == 1)||(prob.GetIdo() == -1)) {

      // Performing matrix-vector multiplication.
      // In shift and invert mode, w = OPv must be performed
      // whenever GetIdo is equal to 1 or -1. GetVector supplies
      // a pointer to the input vector, v, and PutVector a pointer
      // to the output vector, w.

      A.MultOPv(prob.GetVector(), prob.PutVector());

    }
  }

  // Finding eigenvalues and eigenvectors.

  prob.FindEigenvectors();

  // Printing solution.

  Solution(prob);

} // Test.


main()
{

  // Solving a single precision problem with n = 100.

#ifndef __SUNPRO_CC

  Test((float)0.0);

#endif

  // Solving a double precision problem with n = 100.

  Test((double)0.0);

} // main